A maze is designed to confuse you and challenge you to find your way to the exit or to the centre and then back out again. It is designed to test your problem-solving skills, your memory, and your tolerance for frustration!

A labyrinth is designed to give you a single path in and out (so there can be no confusion as to where to go). It is a confined, guided walk with many turns toward a centre. It is designed to let you walk in a compact area while you let your mind relax and meditate.
The confusion probably comes from the mythical labyrinth on Crete which was a maze. The legend about Theseus, Ariadne and the man-eating Minotaur appears to be backed by historical fact. The Minoan culture in Crete that was contemporary with that of the Egyptian Pharaohs, had its power centre at the Palace of Knossos. The legend has it that the Minotaur lived in something called the Labyrinth. When the palace was excavated it proved to have had 300 rooms and a mass of passageways. And the decorations everywhere were of a
two-headed axe, for which the term in Ancient Greek was labros. In other words, the Labyrinth was "The House of the Two-Headed Axe". It really was a maze in both reality and in the myth, but the idea of a labyrinth being a maze has persisted.
There are many parts to a medieval labyrinth and there are appropriate ways to walk it and there are many approaches to meditation using the labyrinth.